A NEW MIXED FINITE-ELEMENT METHOD FOR COMPUTING VISCOELASTIC FLOWS

A new mixed finite element method for computing viscoelastic flows is presented. The mixed formulation is based on the introduction of the r ate of deformation tensor as an additional unknown. Contrary to the po pular EVSS method [D. Rajagopalan, R.A. Brown and R.C. Armstrong, J. N on-Newtonian Fluid Mech., 36 (1990) 159], no change of variable is per formed into the constitutive equation. Hence, the described method can be used to compute solutions of theological models where the EVSS met hod does not apply. The numerical strategy uses a decoupled iterative scheme as a preconditioner for the GMRES algorithm, The stability and the robustness of the method are investigated on two benchmark problem s: the 4:1 contraction flow problem and the stick-slip flow problem. N umerical results for the PTT [N. Phan-Thien and R.I. Tanner, J. Non-Ne wtonian Fluid Mech., 2 (1977) 353] and the Grmela [J. Grmela, J. Rheol ogy, 33 (1989) 207] models show that our method is remarkably stable a nd cheap in computer time and memory.